The Nittany Lions will take on either Florida or Miami in next week's quarterfinals.
Penn State saw a 16-point lead dwindle to six with 2 minutes to play and the Nittany Lions went without a field goal for the final 8:53 of the contest.
They went to the line 17 times in that stretch, however, and made 14 free throws to improve their record to 24-11.
Andrew Jones added 14 points and 10 rebounds for Notre Dame, which made it past the first round of the tournament Tuesday with a win over Alabama-Birmingham.
Rhode Island (23-11) was led by Jimmy Baron with 24 points.